I have had my laptop for a little more than a year, and it's recently begun to do some odd things. It will power down while I'm using it, usually when the power cord is connected. It also doesn't appear to charge when the laptop is plugged in. It used to be where I could wiggle the piece that connects to the computer it would find a place where it could charge the laptop, but now that's not even happening. The fact that it can wiggle leads me to believe it's the jack (most specifically the little metal pin part of the jack) that's causing the laptop to be unable to charge, but I was wondering if the loose jack could also cause it to power down.
It could do yes. If the battery is not charged when the jack moves then the laptop will switch off. You could try holding the jack in position with a couple of thin elastic bands around something, and get another mains wire when you can.